In a large pot over medium heat, melt the butter.

Add the diced onion and cook until translucent, about 5 minutes.

Stir in the minced garlic and cook for an additional minute until fragrant.

Add the sliced mushrooms and dried thyme to the pot. Cook until the mushrooms are tender and have released their juices, about 7 minutes.

Sprinkle the flour over the mushroom mixture, stirring continuously to combine, and cook for 2 minutes to eliminate the raw flour taste.

Gradually pour in the chicken broth while stirring to prevent lumps. Bring the mixture to a boil, then reduce the heat and let it simmer for 10 minutes, allowing the soup to thicken slightly.

Stir in the whole milk and shredded chicken, and cook until heated through, about 5 minutes.

Season the soup with salt and freshly ground black pepper to taste.

Ladle the soup into bowls, garnish with chopped fresh parsley if desired, and serve warm.